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We consider the discrete anisotropic Maxwell operator DaH0 on a bounded paving $\Omega$ $\subset$ Z3 , where H0 denotes discrete isotropic Maxwell operator and Da a diagonal operator of multiplication containing information about the…

Analysis of PDEs · Mathematics 2025-11-18 Olivier Poisson

This paper is concerned with inverse acoustic source problems in an unbounded domain with dynamical boundary surface data of Dirichlet kind. The measurement data are taken at a surface far away from the source support. We prove uniqueness…

Analysis of PDEs · Mathematics 2021-01-22 Guanghui Hu , Yavar Kian , Yue Zhao

In this paper we consider two inverse problems on a closed connected Riemannian manifold $(M,g)$. The first one is a direct analog of the Gel'fand inverse boundary spectral problem. To formulate it, assume that $M$ is divided by a…

Analysis of PDEs · Mathematics 2007-09-17 Katsiaryna Krupchyk , Yaroslav Kurylev , Matti Lassas

This paper is concerned with an inverse wavenumber/frequency-dependent source problem for the Helmholtz equation. In two and three dimensions, the unknown source term is supposed to be compactly supported in spatial variables but…

Numerical Analysis · Mathematics 2024-04-02 Mengjie Zhao , Suliang Si , Guanghui Hu

Redatuming is a data processing technique to transform measurements recorded in one acquisition geometry to an analogous data set corresponding to another acquisition geometry, for which there are no recorded measurements. We consider a…

Analysis of PDEs · Mathematics 2017-10-10 Maarten V. de Hoop , Paul Kepley , Lauri Oksanen

This paper studies an inverse hyperbolic problem for the wave equation with dynamic boundary conditions. It consists of determining some forcing terms from the final overdetermination of the displacement. First, the Fr\'echet…

Analysis of PDEs · Mathematics 2022-12-28 S. E. Chorfi , G. El Guermai , L. Maniar , W. Zouhair

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of…

Analysis of PDEs · Mathematics 2019-06-05 Elena Beretta , Maarten V. de Hoop , Florian Faucher , Otmar Scherzer

We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in $\mathbb{R}^3$ via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann…

Analysis of PDEs · Mathematics 2017-02-10 Maarten V. de Hoop , Gen Nakamura , Jian Zhai

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…

Numerical Analysis · Mathematics 2014-06-11 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu , Otmar Scherzer

In this paper we consider determining a minimal surface embedded in a Riemannian manifold $\Sigma\times \mathbb{R}$. We show that if $\Sigma$ is a two dimensional Riemannian manifold with boundary, then the knowledge of the associated…

Analysis of PDEs · Mathematics 2022-03-18 Cătălin I. Cârstea , Matti Lassas , Tony Liimatainen , Lauri Oksanen

We prove quantitative norm bounds for a family of operators involving impedance boundary conditions on convex, polygonal domains. A robust numerical construction of Helmholtz scattering solutions in variable media via the…

Analysis of PDEs · Mathematics 2022-10-19 Thomas Beck , Yaiza Canzani , Jeremy L. Marzuola

Given the wave equation on a compact Riemannian manifold with boundary, we derive an explicit reconstruction procedure to represent the frequency-domain Neumann-to-Dirichlet map in terms of the time-domain Neumann-to-Dirichlet map at any…

Analysis of PDEs · Mathematics 2026-02-17 Yang Yang

This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general…

Analysis of PDEs · Mathematics 2026-05-28 Dong Qiu , Xiang Xu , Yeqiong Ye , Ting Zhou

We consider the inverse problem for the wave equation on a compact Riemannian manifold or on a bounded domain of $\R^n$, and generalize the concept of {\em domain of influence}. We present an efficient minimization algorithm to compute the…

Analysis of PDEs · Mathematics 2011-01-26 Lauri Oksanen

We consider the restricted Dirichlet-to-Neumann map $\Lambda^{U,V}_{g,A,q}$ for the wave equation with magnetic potential $A$ and scalar potential $q$, on an admissible Lorentzian manifold $(M, g)$ of dimension $n \geq 3$ with boundary.…

Analysis of PDEs · Mathematics 2025-05-21 Yuchao Yi , Yang Zhang

In this paper, we study the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data. Our contributions are twofold: first we introduce a Dirichlet-to-Neumann map for this operator and analyze an associated inverse problem;…

Analysis of PDEs · Mathematics 2026-04-09 Ravi Shankar Jaiswal , Pu-Zhao Kow , Suman Kumar Sahoo

We extend the study of inverse boundary value problems to the setting of fully nonlinear PDEs by considering an inverse source problem for the Monge-Amp\`ere equation \[ \det D^2 u = F. \] We prove that, on a convex Euclidean domain in the…

Analysis of PDEs · Mathematics 2025-10-14 Tony Liimatainen , Yi-Hsuan Lin

After giving a general introduction to the main known results on the anisotropic Calder{\'o}n problem on n-dimensional compact Riemannian manifolds with boundary, we give a motivated review of some recent non-uniqueness results obtained in…

Analysis of PDEs · Mathematics 2018-03-05 Thierry Daudé , Niky Kamran , François Nicoleau

We show that given two hyperbolic Dirichlet to Neumann maps associated to two Riemannian metrics of a Riemannian manifold with boundary which coincide near the boundary are close then the lens data of the two metrics is the same. As a…

Analysis of PDEs · Mathematics 2015-05-13 Plamen Stefanov , Gunther Uhlmann , Andras Vasy

We study the inverse problem for a semilinear wave equation on metric tree graphs. From the Dirichlet-to-Neumann map defined at all but one of the boundary vertices, we recover unknown connectivity of the graph, lengths of the edges, the…

Analysis of PDEs · Mathematics 2026-03-30 Sergei Avdonin , Matti Lassas , Jinpeng Lu , Medet Nursultanov , Lauri Oksanen